Genus bounds for minimal surfaces arising from min-max constructions
Analysis of PDEs
2009-05-26 v1 Differential Geometry
Geometric Topology
Abstract
In this paper we prove genus bounds for closed embedded minimal surfaces in a closed 3-dimensional manifold constructed via min-max arguments. A stronger estimate was announced by Pitts and Rubistein but to our knowledge its proof has never been published. Our proof follows ideas of Simon and uses an extension of a famous result of Meeks, Simon and Yau on the convergence of minimizing sequences of isotopic surfaces. This result is proved in the second part of the paper.
Cite
@article{arxiv.0905.4035,
title = {Genus bounds for minimal surfaces arising from min-max constructions},
author = {Camillo De Lellis and Filippo Pellandini},
journal= {arXiv preprint arXiv:0905.4035},
year = {2009}
}
Comments
Accepted for publication on Journal for Pure and Applied Mathematics